Numerical solution of systems of simultaneous polynomial equations. Technical report SOL 83-10

Technical Report · Fri Jul 01 04:00:00 EDT 1983

OSTI ID:6040673

Rosenberg, A N

A program for finding all real and complex solutions to a system of simultaneous polynomial equations is developed and tested. The program uses a homotopy method to follow paths from solutions of an easy system of equations to solutions of the system of equations being solved. A continuous path-following method takes advantage of the differential information available and does not require the structure of a subdivision to be superimposed on the structure of the problem, as would be the case with a piecewise-linear method. The numerical methods used in the program are chosen empirically. The way an algorithm misbehaves tells about the problem being solved and suggests computational techniques. Problems synthesized by random number generators and problems from other sources are solved by the program. It finds all but a few roots for most systems the size of three quartics in three unknowns or five quadratics in five unknowns. Isolated roots are accurate to machine precision.

• Research Organization: Stanford Univ., CA (USA). Systems Optimization Lab.
• DOE Contract Number: AT03-76ER72018
• OSTI ID: 6040673
• Report Number(s): DOE/ER/72018-T12; ON: DE83015832
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
EQUATIONS
FUNCTIONS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
POLYNOMIALS